Determination of Income and Employment

Aggregate Demand And Its Components

In the context of macroeconomics, particularly in the Keynesian framework, Aggregate Demand (AD) refers to the total planned or desired expenditure on all final goods and services in an economy during a given period. It represents the total demand for goods and services that households, firms, the government, and the rest of the world plan to buy at a given level of income.

In a simple two-sector model of the economy (with only households and firms), the components of aggregate demand are:

1. Consumption Expenditure (C): This is the planned expenditure by households on consumer goods and services.
2. Investment Expenditure (I): This is the planned expenditure by firms on capital goods (like machinery, equipment, buildings) and changes in inventories.

Thus, in a two-sector economy:

$$ AD = C + I $$

In a more realistic four-sector model (including government and the foreign sector), the components are Consumption (C), Investment (I), Government Expenditure (G), and Net Exports (X-M). However, for the basic determination of income and employment, we start with the two-sector model.

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Consumption

Consumption expenditure is the largest component of aggregate demand. The relationship between consumption and income is called the consumption function or propensity to consume. It is based on Keynes's "Fundamental Psychological Law of Consumption," which states that as income increases, consumption also increases, but not by as much as the increase in income.

The Consumption Function

The consumption function shows that consumption has two components:

• Autonomous Consumption ($\bar{C}$): This is the minimum level of consumption that occurs even when income is zero. People need to consume to survive, so they may finance this by drawing down past savings or by borrowing. This component is independent of the level of income.
• Induced Consumption (cY): This is the portion of consumption that depends directly on the level of income. As income (Y) rises, this part of consumption also rises.

The relationship is expressed by the following equation:

$$ C = \bar{C} + cY $$

Where:

• $C$ = Total Consumption Expenditure
• $\bar{C}$ = Autonomous Consumption (and $\bar{C} > 0$)
• $c$ = Marginal Propensity to Consume (MPC)
• $Y$ = Level of National Income

Marginal Propensity to Consume (MPC)

MPC is the rate of change in consumption per unit change in income. It represents the fraction of an additional rupee of income that is consumed.

$$ MPC (c) = \frac{\Delta C}{\Delta Y} $$

Where $\Delta C$ is the change in consumption and $\Delta Y$ is the change in income. The value of MPC lies between 0 and 1 ($0 < c < 1$). For example, if MPC is 0.8, it means that for every additional ₹100 of income, ₹80 will be spent on consumption.

The Savings Function

Since income is either consumed or saved ($Y = C + S$), the savings function can be derived from the consumption function.

$ S = Y - C $

$ S = Y - (\bar{C} + cY) $

$ S = Y - \bar{C} - cY $

$$ S = -\bar{C} + (1-c)Y $$

Where:

• $S$ = Total Savings
• $-\bar{C}$ = Autonomous Savings (or dis-savings). When income is zero, consumption is $\bar{C}$, which must be financed by dis-saving an equal amount.
• $(1-c)$ = Marginal Propensity to Save (MPS)

Marginal Propensity to Save (MPS)

MPS is the rate of change in savings per unit change in income. It represents the fraction of an additional rupee of income that is saved.

$$ MPS (s) = \frac{\Delta S}{\Delta Y} $$

Since any additional rupee of income is either consumed or saved, we have:

MPC + MPS = 1 or $c + s = 1$.

Average Propensities (APC and APS)

• Average Propensity to Consume (APC): The ratio of total consumption to total income ($APC = C/Y$).
• Average Propensity to Save (APS): The ratio of total savings to total income ($APS = S/Y$).

Similarly, since all income is either consumed or saved, we have:

APC + APS = 1

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Investment

Investment refers to the addition to the stock of capital goods, such as machinery, factories, and equipment, as well as changes in inventories. In our analysis, we distinguish between two types of investment:

• Induced Investment: Investment that depends on the level of income or profit. Generally, a higher level of income induces more investment.
• Autonomous Investment ($\bar{I}$): Investment that is not dependent on the level of income. It is influenced by factors external to the model, such as technological changes, population growth, and business expectations (often referred to as 'animal spirits' by Keynes).

For the simple Keynesian model of income determination, we make a simplifying assumption that all investment is autonomous. This means that firms have a fixed investment plan, regardless of the current level of income.

Therefore, the investment function is represented as:

$$ I = \bar{I} $$

Where $\bar{I}$ is a constant, positive amount of investment.

Determination Of Income In Two-Sector Model

The equilibrium level of income and employment in an economy is determined at the point where the total planned spending (Aggregate Demand) equals the total output produced (Aggregate Supply or National Income). In the Keynesian model, since we assume prices are fixed and supply is perfectly elastic, output adjusts to meet the level of aggregate demand. Therefore, equilibrium is determined by aggregate demand.

There are two alternative but equivalent approaches to determine the equilibrium level of income:

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1. Aggregate Demand - Aggregate Supply (AD-AS) Approach

According to this approach, the equilibrium level of income (Y) is determined where planned Aggregate Demand (AD) is equal to Aggregate Supply (AS).

We know that Aggregate Supply is conceptually the same as National Income (AS = Y), as the total value of output produced is distributed as factor incomes.

The equilibrium condition is:

AS = AD

or

Y = C + I

Substituting the functions for C and I, we get:

$$ Y = (\bar{C} + cY) + \bar{I} $$

This equation can be solved for the equilibrium level of income, Y.

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2. Saving - Investment (S-I) Approach

This approach states that the equilibrium level of income is determined where planned savings (S) are equal to planned investment (I).

This condition can be derived directly from the AD-AS approach.

We start with the equilibrium condition:

$ Y = C + I $

Subtracting C from both sides:

$ Y - C = I $

We know that income minus consumption is savings ($Y - C = S$). Therefore:

S = I

This condition makes intuitive sense. Savings is a 'leakage' from the circular flow of income, while investment is an 'injection' into the flow. The economy is in equilibrium when the leakages are exactly equal to the injections. If planned savings were greater than planned investment, it would mean aggregate demand is less than output, leading to unplanned inventory accumulation and a fall in future production. Conversely, if planned investment exceeds planned savings, aggregate demand is greater than output, leading to a rundown of inventories and a rise in future production.

Determination Of Equilibrium Income In The Short Run

Here we will delve deeper into the graphical and algebraic determination of equilibrium income, building upon the two approaches discussed earlier.

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Macroeconomic Equilibrium With Price Level Fixed

A central assumption of the Keynesian theory is that it applies to the short run, an economic environment characterized by:

• Unemployed Resources: The economy is operating below its full potential, meaning there are idle workers and unused factory capacity.
- Fixed Price Level: Because of the excess capacity, firms can increase production without needing to raise prices. Any increase in demand is met by an increase in output, not price. - Perfectly Elastic Aggregate Supply: This is a consequence of the fixed price level. The aggregate supply curve is horizontal up to the full employment level, indicating that firms are willing and able to supply any amount of output demanded at the existing price level.

Under these conditions, the level of output and employment is determined solely by the level of aggregate demand.

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Consumption Function – Graphical Representation

The consumption function $C = \bar{C} + cY$ can be shown graphically.

• The 45° line serves as a reference. At any point on this line, the value on the vertical axis equals the value on the horizontal axis (i.e., C = Y).
• The consumption curve (C) starts from the point $\bar{C}$ on the vertical axis, indicating that consumption is positive even at zero income.
• The curve has a positive slope, which is equal to the MPC (c). Since MPC < 1, the slope of the C curve is less than the slope of the 45° line (which is 1).
• Break-even Point (B): This is where the C curve intersects the 45° line. At this point, C = Y, which means savings are zero. To the left of point B, C > Y (dis-saving). To the right of point B, Y > C (positive saving).

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Investment Function – Graphical Representation

Since we assume investment is autonomous ($I = \bar{I}$), it does not change with the level of income. Graphically, the investment function is a horizontal line parallel to the X-axis. Its height is determined by the fixed level of autonomous investment, $\bar{I}$.

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Aggregate Demand: Graphical Representation

The aggregate demand curve (AD) is derived by vertically adding the autonomous investment (I) to the consumption curve (C).

$AD = C + I = (\bar{C} + cY) + \bar{I} = (\bar{C} + \bar{I}) + cY$

• The AD curve's vertical intercept is the sum of autonomous consumption and autonomous investment $(\bar{C} + \bar{I})$.
• The AD curve has the same slope as the consumption curve (MPC).
• The AD curve is parallel to the consumption curve, with the vertical distance between them being the constant amount of autonomous investment ($\bar{I}$).

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Supply Side Of Macroeconomic Equilibrium

As explained, under the fixed-price assumption, the aggregate supply is determined by aggregate demand. The AS curve is represented by the 45-degree line from the origin. This line represents all points where total spending (on the Y-axis) is equal to total income/output (on the X-axis). Thus, the condition AS = Y is embodied in this line.

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Equilibrium

The equilibrium level of income and output is determined where the AD curve intersects the AS (45°) line. At this point (E), planned aggregate demand is exactly equal to the total output of the economy.

Algebraic Determination

Equilibrium condition: $ Y = AD $

$ Y = C + I $

$ Y = \bar{C} + cY + \bar{I} $

To solve for Y, we gather all terms with Y on one side:

$ Y - cY = \bar{C} + \bar{I} $

$ Y(1 - c) = \bar{C} + \bar{I} $

Let $\bar{A} = \bar{C} + \bar{I}$ be the total autonomous expenditure. Then:

$$ Y^* = \frac{\bar{C} + \bar{I}}{1 - c} = \frac{\bar{A}}{1 - c} $$

This equation gives the equilibrium level of income.

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Effect Of An Autonomous Change In Aggregate Demand On Income And Output

Suppose there is an increase in autonomous expenditure, for instance, firms decide to increase their autonomous investment by an amount $\Delta\bar{I}$. This will shift the aggregate demand curve upwards by $\Delta\bar{I}$, from AD to AD'. The economy will move to a new equilibrium point (E'), resulting in a higher level of equilibrium income (Y').

A key observation from the graph is that the increase in income ($\Delta Y = Y' - Y^*$) is larger than the initial increase in investment ($\Delta\bar{I}$). This magnified effect on income is due to the multiplier mechanism.

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The Multiplier Mechanism

The investment multiplier (k) is the ratio of the total change in equilibrium income to the initial change in autonomous investment.

$$ k = \frac{\Delta Y}{\Delta I} $$

The multiplier process works because one person's expenditure is another person's income. When investment increases, it creates income for those who produce the investment goods. These people then spend a portion of their new income (determined by the MPC), which creates income for others. This process continues in successive rounds, with each round of spending being smaller than the previous one.

Derivation of the Multiplier

We know the equilibrium equation is $Y = \frac{\bar{A}}{1 - c}$.

If autonomous spending changes by $\Delta \bar{A}$, the income will change by $\Delta Y$. The new income $Y'$ will be:

$ Y' = \frac{\bar{A} + \Delta\bar{A}}{1 - c} = \frac{\bar{A}}{1-c} + \frac{\Delta\bar{A}}{1-c} $

The change in income is:

$ \Delta Y = Y' - Y = \left( \frac{\bar{A}}{1-c} + \frac{\Delta\bar{A}}{1-c} \right) - \frac{\bar{A}}{1-c} = \frac{\Delta\bar{A}}{1-c} $

$ \Delta Y = \Delta\bar{A} \times \frac{1}{1-c} $

The multiplier, $k = \frac{\Delta Y}{\Delta\bar{A}}$, is therefore:

$$ k = \frac{1}{1 - c} = \frac{1}{1 - MPC} = \frac{1}{MPS} $$

The size of the multiplier depends directly on the MPC. A higher MPC means a larger portion of new income is re-spent in each round, leading to a larger multiplier effect. A lower MPC (and higher MPS) means more of the new income 'leaks' out into savings, resulting in a smaller multiplier.

Answer:

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Paradox Of Thrift

The "paradox of thrift" is a counter-intuitive result from Keynesian economics. It states that if society as a whole decides to become more thrifty (i.e., they attempt to save more at any given level of income), their collective attempt may fail. The total savings of the economy might not increase, and in fact, the economy could be worse off with a lower level of income.

Explanation

1. An attempt to save more is equivalent to an attempt to consume less.
2. A decrease in consumption expenditure leads to a decrease in aggregate demand (the AD curve shifts down).
3. This fall in AD, through the multiplier process, leads to a fall in the equilibrium level of income and output.
4. Since saving depends on income, the fall in income will lead to a decrease in the actual amount of saving.

In the S-I framework, an increased desire to save shifts the savings curve upwards (from S to S'). With autonomous investment (I) remaining fixed, the new equilibrium (E') occurs at a lower level of income (Y'). At this new equilibrium, the amount of saving is still equal to the fixed investment ($\text{S'} = \bar{I}$). So, while the propensity to save has increased, the total amount of saving has remained the same, but at the cost of a lower national income and higher unemployment.

This is a paradox because what seems virtuous for an individual (saving more) can be detrimental to the economy as a whole if everyone does it simultaneously.

Some More Concepts

The Keynesian model of income determination helps us understand situations where the economy is not at full employment and analyze the gap between the actual equilibrium and the full employment equilibrium.

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Full Employment and Involuntary Unemployment

• Full Employment: This refers to a situation in which all those who are willing and able to work at the prevailing wage rate are able to find employment. It does not mean a zero rate of unemployment, as there will always be some level of frictional (people between jobs) and structural (mismatch of skills) unemployment. Full employment corresponds to the maximum potential output level of the economy ($Y_F$).
• Involuntary Unemployment: This is a situation where able-bodied workers are willing to work at the current wage rate but cannot find jobs. This is the type of unemployment that arises due to a deficiency in aggregate demand. The equilibrium of the economy can occur at a level of income below full employment, leading to involuntary unemployment.

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Inflationary Gap

An inflationary gap exists when the actual aggregate demand is more than the aggregate supply corresponding to the full employment level of output.

$$ AD > AS \text{ (at the full employment level)} $$

This situation arises when the equilibrium income determined by AD = AS is higher than the full employment income. Since the economy is already at its maximum potential output, this excess demand cannot be met by increasing production. Instead, it pulls up the general price level, leading to inflation.

The gap is the vertical distance between the actual AD curve and the 45° line at the full employment level of income. It measures the amount of excess demand.

To correct this, a government would pursue a contractionary fiscal policy (e.g., reduce government spending, increase taxes) or the central bank would pursue a contractionary monetary policy (e.g., raise interest rates) to reduce aggregate demand.

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Deflationary Gap (Recessionary Gap)

A deflationary gap exists when the actual aggregate demand is less than the aggregate supply corresponding to the full employment level of output.

$$ AD < AS \text{ (at the full employment level)} $$

This situation arises when the equilibrium level of income is below the full employment level. This deficiency in demand leads to involuntary unemployment and a fall in output, pushing the economy into a recession. Firms have unsold goods, leading them to cut back on production and employment.

The gap is the vertical distance between the actual AD curve and the 45° line at the full employment level of income. It measures the amount by which autonomous spending must be increased to reach full employment.

To correct this, a government would pursue an expansionary fiscal policy (e.g., increase government spending, cut taxes) or the central bank would pursue an expansionary monetary policy (e.g., lower interest rates) to boost aggregate demand and close the gap.

Key Concepts

• Aggregate Demand (AD): Total planned expenditure on final goods and services in an economy. In a two-sector model, AD = C + I.
• Aggregate Supply (AS): The total value of final goods and services produced in an economy, which is equal to national income (Y).
• Consumption Function: The functional relationship between consumption and income ($C = \bar{C} + cY$).
• Autonomous Consumption ($\bar{C}$): The level of consumption when income is zero.
• Marginal Propensity to Consume (MPC or c): The fraction of additional income that is consumed ($\Delta C / \Delta Y$).
• Savings Function: The functional relationship between saving and income ($S = -\bar{C} + (1-c)Y$).
• Marginal Propensity to Save (MPS or s): The fraction of additional income that is saved ($\Delta S / \Delta Y$).
• Autonomous Investment ($\bar{I}$): Investment that is independent of the level of income.
• Equilibrium Income: The level of income where aggregate demand equals aggregate supply (AD = AS) or where planned saving equals planned investment (S = I).
• Ex-ante Variables: Planned or intended values of variables (e.g., ex-ante consumption, ex-ante investment). Keynesian theory is based on ex-ante concepts.
• Ex-post Variables: Actual or realised values of variables (e.g., ex-post savings).
• Investment Multiplier (k): The ratio of the change in equilibrium income to the change in autonomous spending ($k = \Delta Y / \Delta I = 1/(1-MPC)$).
• Paradox of Thrift: The proposition that an attempt by the society to save more may result in the same or even less total saving, due to a fall in the equilibrium level of income.
• Full Employment: A situation where all those willing and able to work at the prevailing wage rate get work.
• Involuntary Unemployment: Unemployment that exists because of a deficiency of aggregate demand.
• Inflationary Gap: The amount by which aggregate demand exceeds aggregate supply at the full employment level.
• Deflationary Gap: The amount by which aggregate demand falls short of aggregate supply at the full employment level.

Summary

The theory of determination of income and employment, primarily based on the work of John Maynard Keynes, explains how the equilibrium level of output and jobs is established in an economy in the short run. The core tenet of this theory is that the level of economic activity is determined by the level of aggregate demand, under the assumption of a fixed price level and excess capacity.

Aggregate demand (AD) in a simple two-sector economy is the sum of planned consumption (C) and planned investment (I). The consumption function ($C = \bar{C} + cY$) shows that consumption depends on autonomous factors ($\bar{C}$) and the level of income (Y), with the Marginal Propensity to Consume (MPC) determining the slope. The corresponding savings function is $S = -\bar{C} + (1-c)Y$. For simplicity, investment is assumed to be autonomous ($\bar{I}$), meaning it is a fixed amount independent of income.

The equilibrium level of income is determined where aggregate demand equals aggregate supply (AD = AS or Y = C+I) or, alternatively, where planned leakages equal planned injections (S = I). This equilibrium may or may not be at the full employment level of output. If the equilibrium occurs below full employment, it results in a deflationary (or recessionary) gap and involuntary unemployment. If aggregate demand exceeds the economy's productive capacity, it creates an inflationary gap, leading to rising prices.

A crucial concept is the investment multiplier ($k = 1/(1-MPC)$), which explains how an initial change in autonomous spending (like investment or government expenditure) leads to a much larger change in the total national income. This amplified effect is central to understanding business cycles and the impact of fiscal policy.

The theory also presents the paradox of thrift, which suggests that an attempt by everyone to save more can, paradoxically, reduce national income without increasing total national savings, highlighting how individual rationality can sometimes lead to collective irrationality in macroeconomics.